Hemodialysis (or simply dialysis) is a process which employs an artificial kidney to aid patients whose renal function has deteriorated to the point where their body cannot adequately rid itself of toxins. In hemodialysis a dialyzer is used which contains a semi-permeable membrane, the membrane serving to divide the dialyzer into two chambers. Blood is pumped through one chamber and a dialysis solution through the second. As the blood flows by the dialysis fluid, impurities, such as urea and creatinine, diffuse through the semi-permeable membrane into the dialysis solution. The electrolyte concentration of the dialysis fluid is set so as to maintain electrolytic balance within the patient.
Further purification in an artificial kidney is possible through ultrafiltration. Ultrafiltration results from the normal situation wherein there is a positive pressure differential between the blood and the dialysis fluid chambers. This pressure differential causes water in the blood to pass through the membrane into the dialysis solution. This provides the benefit of reducing a dialysis patient's excess water load which normally would be eliminated through proper kidney functioning.
Typically, an arterio-venous shunt, frequently termed a “fistula,” is surgically inserted between a patient's artery and vein to facilitate transfer of blood from the patient to the dialyzer. During a normal dialysis treatment, one end of an arterial line or tube is inserted into the upstream end of the fistula (i.e., at a point near the patient's artery) and transports blood withdrawn from the upstream portion of the fistula to the inlet of the dialyzer; a venous line or tube connected to the output of the blood side of the dialyzer returns treated blood to the fistula at an insertion point downstream of the arterial line (i.e., at a point nearer the patient's vein).
Successful dialysis treatment requires knowledge of several hemodialysis parameters in order to optimize the overall efficacy of the dialysis procedure, to assess the condition of the fistula and to determine the actual purification achieved. One key measure of dialysis efficiency is described by the ratio Kt/V, where K is the clearance or dialysance (both terms representing the purification efficiency of the dialyzer), t is treatment time and V is the patient's total water volume. Studies have demonstrated that patient survival increases when the Kt/V ratio has a value of 0.8 or greater (Gotch, F. A. & Sargent, S. A. “A Mechanistic Analysis of the National Cooperative Dialysis Study.” Kidney International., Vol. 28, pp. 526–34 (1985)). The water volume of the patient, V, can be estimated from a patient's weight, age, sex and percentage of body fat. Hence, with knowledge of clearance, K, it is possible to determine the time, t, for optimal dialysis treatment according to the above relationship.
Dialysance or clearance, as noted above, is a measure of the purification efficiency of the dialyzer. More specifically, dialysance is a measure of the volume of blood cleared of urea or some other solute within a certain time period. Hence, one way to determine dialysance is to make in-vivo urea concentration measurements. This is a time-consuming approach, since it requires that samples be withdrawn and analyzed in a laboratory. Alternatively, sodium chloride dialysance or clearance can be measured, since it is known that the clearance of sodium chloride is equivalent to urea clearance. Because sodium and chloride ions comprise essentially all the electrolytes giving rise to the conductivity of both blood and the dialysis solution, dialysance or clearance can simply be determined by making conductivity measurements.
As shown by Sargent, J. A. and Gotch, F. A. (“Principles and Biophysics of Dialysis,” in: Replacement of Renal Function by Dialysis, (W. Drukker, et al., Eds.), Nijoff The Hague (1983) incorporated herein by reference), it is possible to define dialysance in terms of concentrations at the inlet and outlet to the blood side of the dialyzer, the inlet to the dialysis solution side of the dialyzer and the blood flow rate according to the following equation:
                    D        =                  Qb          ⁢                                    Cbi              -              Cbo                                      Cbi              -              Cdi                                                          (        1        )            
where:                Cbi=blood inlet concentration        Cbo=blood outlet concentration        Qb=blood flow rate        D=dialysance        Cdi=dialysis fluid inlet concentration        Cdo=dialysis fluid outlet concentration        
As demonstrated in U.S. Pat. No. 5,100,554 to Polaschegg, this equation can be rewritten strictly in terms of dialysis solution concentrations. In particular, from mass balance based upon flow across the dialysis membrane, the following relationship can be established:Qb(Cbi−Cbo)=Qd(Cdi−Cdo)  (2)
Thus, it is possible from equations (1) and (2) to rewrite equation (1) without a Cbo term as follows:

where:                Qd=dialysis flow rate; the rest of the terms are as defined for equation (1).        
In equation (3), the terms Qd and Cdi are known and a value for Cdo can be easily determined by placing a detector at the dialysis solution outlet of the dialyzer. This leaves D and Cbi as the only unknown values. Using two dialysis solutions having different initial concentrations of a substance, it is possible to write two equations with two unknowns and solve for dialysance, as shown in the following equation:
                    D        =                  Qd          ⁢                                                    (                                  Cdi1                  -                  Cdo1                                )                            -                              (                                  Cdi2                  -                  Cdo2                                )                                                    Cbi1              -              Cdi2                                                          (        4        )            
where:                D=dialysance        Qd=dialysis flow rate        Cdi1=concentration of substance upstream of dialyzer, first dialysis solution        Cdi1=concentration of substance downstream of dialyzer, first dialysis solution        Cdi2=concentration of substance upstream of dialyzer, second dialysis solution        Cdo2=concentration of substance downstream of dialyzer, second dialysis solution        
Other methods and apparatus for determining dialysance are described in U.S. Pat. No. 5,024,756 to Sternby, U.S. Pat. Nos. 5,567,320 to Goux, and U.S. Pat. No. 4,668,400 to Veech, as well as European Patents EP 330,892B1 and EP 547,025B1 to Sternby and European Patent Application 547,025A1 by Sternby.
Blood access flow rate is another hemodialysis parameter which is of critical importance in optimizing dialysis procedures and in monitoring the general condition of the fistula. Blood access flow rate is defined as the blood flow rate at the entrance to the fistula as the blood flows in from a patient's artery. Blood access flow rate is important for at least two reasons. First, with time it is possible for the fistula to become clotted or stenose. Hence, flow rate can serve as an indicator of changes in the integrity of the fistula: Secondly, the rate of access flow relative to dialyzer flow rate affects recirculation, the phenomenon whereby treated blood from the venous line commingles with untreated blood in the fistula and is drawn into the arterial line and then carried back to the dialyzer. It can readily be appreciated that as recirculation increases the efficiency of the dialysis procedure decreases, since recirculation results in treated blood being retreated. Recirculation increases when the blood flow rate through the fistula is insufficient relative to the blood flow rate through the dialyzer. Thus, a knowledge of access flow rate is also important in assessing the degree to which recirculation occurs and in selecting flow rates for pumping blood through the dialyzer.
Several methods are known for determining access flow rates. However, these methods all suffer from a critical limitation, namely that the determination depends upon blood concentrations of some solute or added solution. As a consequence, the methods are invasive, tending to require the withdrawal of blood samples or the injection of solutions into the patient's blood stream.
One such method, the color-coded duplex sonography method has found utility in identifying patients at risk for access failure (Sands, J. et al., “The Effect of Doppler Flow Screening Studies and Elective Revisions on Dialysis Failure.” ASAIO Journal, Vol. 38, pp. 524–527 (1992)). The method, however, is only rarely used because of its expense, the requirement for trained personnel and the fact that results vary depending upon operating conditions (see for example, Wittenberg, G. et al. “Interobserver Variability of Dialysis Shunt Flow Measurements using Color Coated Duplex Sonography.” Rofo Fortschr Geb Rontgenstr Neuen Bildgeb Verfahr, Vol. 154, pp. 375–378 (1993) and Oates, C. P., et al. “The use of Diasonics DRF400 Duplex Sound Scanner to Measure Blood Flow in ArteriovenouslFistulae in Patients Undergoing Hemodialysis: An Analysis of Measurement Uncertainties.” Ultrasound Med. Biol., Vol. 16, pp.571–579, (1990)).
Other approaches are based upon dilution methods and require the injection of a volume of a solution having a characteristic distinct from blood (often called a “bolus”) into either the arterial or venous line which is connected to the patient's fistula. A general method for determining flow rates in tubes is described in U.S. Pat. No. 5,644,240 by Brugger. This method involves the injection of a saline bolus and the subsequent monitoring of changes in electrical conductivity in a patient's blood line.
A related method requires the reversal of the arterial and venous lines so that the venous line is upstream of the arterial line, the injection of a saline bolus into one of the blood lines and then detection of the alteration of the sound velocity characteristics of the blood by ultrasound methods. This method is described in: U.S. Pat. Nos. 5,685,989, 5,595,182 and 5,453,576 to Krivitski; PCT application WO 96/083 05 A1 by Krivitski; and in a publication by Nikolai Krivitski (“Theory and Validation of Access Flow Measurement by Dilution Technique during Hemodialysis.” Kidney International, Vol. 48, pp. 244–250 (1995)). These methods suffer from their invasive nature, namely the requirement that a foreign mixture be injected into the patient's bloodstream and, in some cases, the insertion of sensors into a patient's vascular system (U.S. Pat. Nos. 5,595,182 and 5,453,576 to Krivitski). Furthermore, the injection requirement for these methods makes these approaches relatively cumbersome; such methods also do not lend themselves to automation.
There are similar shortcomings to current methods for calculating recirculation. Like methods for determining blood access flow rates, present procedures require measurements on the blood side of the dialyzer and thus are invasive in nature. Often the methods require injection of a foreign solution into the blood stream (U.S. Pat. Nos. 5,570,026, 5,510,717 and 5,510,716 to Buffaloe, IV, et al.; U.S. Pat. No. 5,644,240 to Brugger; U.S. Pat. No. 5,685,989 to Krivitski, et al., U.S. Pat. Nos. 5,595,182 and 5,453,576 to Krivitski; and U.S. Pat. No. 5,312,550 to Hester).
In contrast to these invasive techniques, a method using dialysis solution concentration measurements only has been developed to determine a patient's blood sodium level (U.S. Pat. No. 4,923,613 to Chevallet). Related methods have been developed in which the effect of variations in solute concentration in dialysis solutions are determined. Results are used to develop a profile to optimize dialysis conditions to the patient's needs (U.S. Pat. Nos. 5,662,806 and 5,518,623 to Keshaviah, et al. and U.S. Pat. No. 5,507,723 to Keshaviah).
Several dialysis apparatus have been developed to monitor changes in dialysis solution composition, including U.S. Pat. No. 4,508,622 to Polaschegg and U.S. Pat. No. 5,024,756 to Sternby and European Patents 097,366 A2 to Polaschegg; 330,892 B1 and 547,025 B1 to Sternby; as well as European Patent Application 272,414 A2 to Polaschegg.
However, there remains a need for a method and apparatus for determining hemodialysis parameters such as blood access flow rates and recirculation by non-invasive methods that do not require that measurements be made on the blood side of the dialyzer. The methods and apparatus of the present invention satisfy such a need by providing for the first time an approach for determining hemodialysis parameters such as blood access flow rate and recirculation solely from concentration measurements taken on the dialysate side of the dialyzer, thereby providing a non-invasive means for determining such parameters.